Data Analysis and Probability Standard Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions andarguments that are based on data.
By the end of the 3-4 program:
A. Gather and organize data from surveys and classroom experiments, including data collected over a period of time.
B. Read and interpret tables, charts, graphs (bar, picture, line, line plot), and timelines as sources of information, identify main idea, draw conclusions, and make predictions.
C. Construct charts, tables and graphs to represent data, including picture graphs, bar graphs, line graphs, line plots and Venn diagrams.
D. Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one; e.g., each = 10 bicycles or the intervals on an axis are multiples of 10.
E. Describe data using mode, median and range.
F. Conduct a simple probability experiment and draw conclusions about the likelihood of possible outcomes.
G. Identify and represent possible outcomes, such as arrangements of a set of up to four members and possible combinations from several sets, each containing 2 or 3 members.
H. Use the set of possible outcomes to describe and predict events.
By the end of the 5-7 program:
A. Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.
B. Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.
C. Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.
D. Compare increasingly complex displays of data, such as multiple sets of data on the same graph.
E. Collect, organize, display and interpret data for a specific purpose or need.
F. Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.
G. Evaluate conjectures and predictions based upon data presented in tables and graphs, and identify misuses of statistical data and displays.
H. Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.
I. Describe the probability of an event using ratios, including fractional notation.
J. Compare experimental and theoretical results for a variety of simple experiments.
K. Make and justify predictions based on experimental and theoretical probabilities.
By the end of the 8-10 program:
A. Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
B. Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.
C. Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.
D. Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.
E. Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.
F. Construct convincing arguments based on analysis of data and interpretation of graphs.
G. Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
H. Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
I. Design an experiment to test a theoretical probability, and record and explain results.
J. Compute probabilities of compound events, independent events, and simple dependent events.
K. Make predictions based on theoretical probabilities and experimental results.
Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data.
By the end of the 3-4 program:
By the end of the 5-7 program:
By the end of the 8-10 program:
Examples:
3rd Grade/Creating a Bar Graph
http://nces.ed.gov/nceskids/createagraph/
8th Grade/Creating Box and Whisker Graph
http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html